1–
13.
Two Indiana state senate candidates must decide which city to visit the day before the November election. The same four cities–Indianapolis, Evansville, Fort Wayne, and South
Bend-are available for both candidates. These cities are listed as strategies 1 to 4 for each
~andidate. Travel plans must be made in advance, so the candidates must decide which city
to visit prior to knowing the other candidate’s plans. Values in the following table show
thousands of voters for the Republican candidate based on the strategies selected by the two
candidates. Which city should each candidate visit, and what is the value of the game?
Democrat Candidate
Indianapolis
bI
Republican
Candidate
192
Chapter 5
Indianapolis, aj
Evansville, a2
Fort Wayne, ~
South Bend, a4
o
Evansville
h2
-15
Fort
Wayne
b3
South
Bend
b4
-8
30
10
-25
20
o
20
20
10
-5
5
-10
Utility and Game Theory
15. In a gambling game, Player A and Player B both have a $1 and a $5 bilL Each player
selects one of the bills without the other player knowing the bill selected. Simultaneously
they both reveal the bills selected. If the bills do not match, Player A wins Player B’ s bill.
If the bills match, Player B wins Player A’s bill.
a. Develop the game theory table for this game. The values should be expressed as the
gains (or losses) for Player A.
b. Is there a pure strategy? Why or why not?
c. Determine the optimal strategies and the value of this game. Does the game favor one
player over the other?
d. Suppose Player B decides to deviate from the optimal strategy and begins playing
each bill 50% of the time. What should Player A do to improve Player A’s winnings?
Comment on why it is important to follow an optimal game theory strategy.
20
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